Probability and quanta: why back to Nelson?

Piotr Garbaczewski

Banach Center Publications (1998)

  • Volume: 43, Issue: 1, page 191-199
  • ISSN: 0137-6934

Abstract

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We establish circumstances under which the dispersion of passive contaminants in a forced flow can be consistently interpreted as a Markovian diffusion process.

How to cite

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Garbaczewski, Piotr. "Probability and quanta: why back to Nelson?." Banach Center Publications 43.1 (1998): 191-199. <http://eudml.org/doc/208838>.

@article{Garbaczewski1998,
abstract = {We establish circumstances under which the dispersion of passive contaminants in a forced flow can be consistently interpreted as a Markovian diffusion process.},
author = {Garbaczewski, Piotr},
journal = {Banach Center Publications},
keywords = {diffusion processes; partial differential equations; stochastic mechanics},
language = {eng},
number = {1},
pages = {191-199},
title = {Probability and quanta: why back to Nelson?},
url = {http://eudml.org/doc/208838},
volume = {43},
year = {1998},
}

TY - JOUR
AU - Garbaczewski, Piotr
TI - Probability and quanta: why back to Nelson?
JO - Banach Center Publications
PY - 1998
VL - 43
IS - 1
SP - 191
EP - 199
AB - We establish circumstances under which the dispersion of passive contaminants in a forced flow can be consistently interpreted as a Markovian diffusion process.
LA - eng
KW - diffusion processes; partial differential equations; stochastic mechanics
UR - http://eudml.org/doc/208838
ER -

References

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  1. [1] Ph. Blanchard and P. Garbaczewski, Natural boundaries for the Smoluchowski equation and affiliated diffusion processes, Phys. Rev. E 49, (1994), 3815. 
  2. [2] K. L. Chung and Z. Zhao, From Brownian Motion to Schrödinger Equation, Springer-Verlag, Berlin, 1995. Zbl0819.60068
  3. [3] M. Freidlin, Functional Integration and Partial Differential Equations, Princeton University Press, Princeton, 1985. 
  4. [4] P. Garbaczewski, J. R. Klauder and R. Olkiewicz, Schrödinger problem, Lévy processes, and noise in relativistic quantum mechanics, Phys. Rev. E 51, (1995), 4114. 
  5. [5] P. Garbaczewski and R. Olkiewicz, Feynman-Kac kernels in Markovian representations of the Schrödinger interpolating dynamics, J. Math. Phys. 37, (1996), 730. Zbl0869.60101
  6. [6] P. Garbaczewski, Schrödinger's interpolation problem through Feynman-Kac kernels, Acta Phys. Polon. B 27, (1996), 617. Zbl0966.82512
  7. [7] P.Garbaczewski and G. Kondrat, Burgers velocity fields and dynamical transport processes, Phys. Rev. Lett. 77, (1996), 2608. 
  8. [8] P. Garbaczewski, G. Kondrat and R. Olkiewicz, Burgers flows as Markovian diffusion processes, Phys. Rev. E 55, (1997), 1401. Zbl0939.35201
  9. [9] W. Horsthemke and R. Lefever, Noise-Induced Transitions, Springer-Verlag, Berlin, 1984. Zbl0529.60085
  10. [10] C. Marchioro and M. Pulvirenti, Vortex methods in Two-Dimensional Fluid Dynamics, Lecture Notes in Physics 203, Springer-Verlag, Berlin, 1984. Zbl0545.76027
  11. [11] E. Nelson, Dynamical Theories of the Brownian Motion, Princeton University Press, Princeton, 1967. Zbl0165.58502
  12. [12] H. Spohn, Large Scale Dynamics of Interacting Particles, Springer-Verlag, Berlin, 1992. Zbl0742.76002
  13. [13] H. Risken, The Fokker-Planck Equation, Springer-Verlag, Berlin, 1989. Zbl0665.60084
  14. [14] E. Schrödinger, Relativistic electron, Ann. Inst. Henri Poincaré, 2, (1932), 269. 
  15. [15] J. C. Zambrini, Variational processes and stochastic versions of mechanics, J. Math. Phys. 27, (1986), 3207. Zbl0623.60102

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